This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A329261 #4 Nov 09 2019 16:29:00
%S A329261 0,0,1,1,3,11,40,232,1246,8912,65766,561001,5198424,52513111,
%T A329261 577791292,6806860347,86303601008,1163845620633,16701819148776,
%U A329261 253608108810052,4065574363467636,68608467057149112,1215544196988580438,22564088376584800717
%N A329261 Expansion of e.g.f. -log(1 - Sum_{k>=1} x^prime(k) / prime(k)!).
%F A329261 a(0) = 0; a(n) = A010051(n) + (1/n) * Sum_{k=1..n-1} binomial(n,k) * A010051(n-k) * k * a(k).
%t A329261 nmax = 23; CoefficientList[Series[-Log[1 - Sum[x^Prime[k]/Prime[k]!, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%t A329261 a[n_] := a[n] = Boole[PrimeQ[n]] + Sum[Binomial[n, k] Boole[PrimeQ[n - k]] k a[k], {k, 1, n - 1}]/n; a[0] = 0; Table[a[n], {n, 0, 23}]
%Y A329261 Cf. A000629, A010051, A190476, A305618, A305619.
%K A329261 nonn
%O A329261 0,5
%A A329261 _Ilya Gutkovskiy_, Nov 09 2019